Roof Pitch Calculator

How to calculate roof pitch from a rise and run measurement

Roof pitch is the rise divided by the run, multiplied by 12 for the X-in-12 label a plan carries. Measured on the roof itself, a roofer holds a two-foot level flat against the underside of a rafter, marks 12 inches along it from the contact point, then measures straight down to the roof plane. The inches on the tape are the rise while the horizontal 12 inches are the run, so 6 inches of drop over that run gives a 6/12 pitch.

Anyone trying to figure roof pitch without climbing up works from the ground instead. The ridge height above the wall plate divided by half the building width gives the same answer, the run of a gable being half its span. On a house 28 feet wide whose ridge sits 7 feet above the plate, the run is 14 feet and 7 divided by 14 gives a slope of 0.5, so the calculator returns 6/12 at 26.57 degrees with a 15.65 ft rafter before any overhang.

How to calculate roof pitch in degrees and in percent

The angle is the arctangent of the rise divided by the run, one keystroke on any scientific calculator. On a 4/12 roof, 4 divided by 12 gives a slope of 0.3333, whose arctangent is 18.43 degrees while the same 0.3333 multiplied by 100 gives 33.33 percent.

Percent and degrees only track each other near the bottom of the scale. A 100 percent slope works out to 45 degrees, percent counting rise against run while degrees measure the angle off the horizontal. A reading of 30 degrees on an inclinometer is a 6.93/12 pitch at 57.74 percent.

Metric drawings and digital inclinometers give slope in percent, so a 45 percent reading converts to 5.4/12 at 24.23 degrees, the X-in-12 label a framer or a shingle supplier will ask for.

Roof pitch angle chart from 1/12 to 12/12

Most plans call for a whole number of inches of rise, so the roof pitch angle chart below lists every rise from 1/12 to 12/12 with its angle, its percentage and its area multiplier. That last column is the square root of 1 plus the slope squared, which doubles as the rafter length per unit of run.

The rows change the material bill more than the method, the step from 4/12 to 8/12 adding about 14 percent to the surface to cover, 1.2019 against 1.0541.

What a 22.5 degree roof and a 45 degree angle work out to

A 22.5 degree roof is a 5/12 pitch in every practical sense. The exact arithmetic falls a fraction short, tan(22.5°) × 12 working out to 4.97 in 12 against the 22.62 degrees of a true 5/12, a gap no slope gauge resolves on a finished deck. A roof read at 22.5 degrees gets framed and ordered as 5/12 at 41.42 percent.

A 45 degree angle is the one pitch where all three notations land on whole numbers, 12/12 with the rise equal to the run and a slope of exactly 100 percent. Its rafters run 1.4142 times the horizontal run, the square root of 2, so the roof surface covers 41 percent more area than the footprint beneath it.

Minimum roof pitch for shingles and the point a roof stops being walkable

The wrapper on a bundle of asphalt shingles prints a minimum slope, usually 2/12. Below that line the shingles stop holding water because wind driven rain climbs back under the tabs faster than the slope sheds it. The residential code (IRC R905.2.2) draws the same 2:12 floor and sends anything flatter to a membrane, either EPDM, TPO or torch applied modified bitumen.

Between 2/12 and 4/12 shingles are allowed with the underlayment doubled over the whole deck, a single layer being enough above 4/12. Those figures are code minimums. The installation instructions printed on the bundle govern the warranty. A product that asks for more slope or for extra sealing at the eaves sets the number to build to.

Access to the deck changes at 6/12, the last pitch a roofer walks in soft soled shoes without staging. Past that point the quote picks up roof jacks, planks and a harness on rated anchor points, all labour rather than material. Above 9/12 scaffolding becomes the norm and the pace of loading bundles drops.

Steepness shows up again on the material order. A 10/12 deck covers 1.3017 times its footprint, close to a third more shingle than a ground area estimate suggests. On a 2,000 sq ft footprint the difference is 603 sq ft of extra surface, roughly six more squares, a square being the 100 sq ft unit roofing is sold in.